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Infinity doesn't have a value. It's an ideal number. This means it does not occupy a point on the real line. It occupies a position similar to that of the extra point in the projective plane (the one at which parallel lines meet).

One way of visualising how this works is like this (This was explained to me when I was jet-lagged out of my mind and still made some sense. it must be good.):

Imagine the complex plane as a flat plane in 3-dimensional space. Imagine a sphere resting on this plane so that the bottom of the sphere just touches the point representing zero. One can visualise a mapping from each point P on the plane to a point P' on the sphere. Simply draw a line from the top of the sphere I, through P. The other point at which IP cuts the sphere is P'.

Obviously there exists a P' for every P and there exists a P for every P' except I. The number which would map to I is infinity. As you can see, this explains why minus infinity equals plus infinity, something I never understood before.

I hope this helps people get a handle on infinity. It may make no sense at all, but hey, it's infinity, it never made sense in the first place.

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